Floating-point multiplication capability may be provided in a data processing apparatus. The floating-point format for numbers is useful to be supported, in particular in view of the large range of values which it is able to represent. Accordingly, a data processing apparatus may be provided with a floating-point multiplier which is specifically provided for the purpose of handling the multiplication of such floating-point values. Various aspects of the implementation of such a floating-point multiplier are nevertheless non-trivial, especially if the multiplier is to operate quickly and efficiently, and these complexities are greater the more flexibility is allowed in the representation of an operand for the floating-point multiplication which the multiplier receives. For example, the construction of the floating-point multiplier may be simplified by constraining the representation of input operands to normalised inputs, yet more generally the floating-point values which a data processing apparatus is required to handle will not necessarily conform to this normalised representation and therefore additional capability in the input stages of the multiplier then needs to be provided to convert non-normalised inputs into a normalised representation. It would be desirable to provide an improved technique for handling floating-point multiplication in a data processing apparatus.